Answer
Longer side: $12.5\text{ cm}$
Hypotenuse: $13.5\text{ cm}$
Work Step by Step
Let $x$ be the longer side. Since the ratio of the longer side and the shorter side is $2.5$, then
$$\begin{aligned}
\frac{x}{5}&=2.5
\\
x&=12.5
.\end{aligned}$$Hence, the longer side is $12.5\text{ cm}$ long.
Using $a^2+b^2=c^2$ or the Pythagorean Theorem, with legs equal to $5$ and $12.5$ cm long then
$$\begin{aligned}
5^2+12.5^2&=c^2
\\
c^2&=181.25
\\
c&\approx13.5
.\end{aligned}$$Hence, the hypotenuse is approximately $13.5\text{ cm}$ long.
